Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


## NULL

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_black 2 1.636775
beta3_pH 3 1.628981
beta0_black 1 1.611379
beta2_pelagic 9 1.498027
beta2_black 6 1.490472
beta1_black 12 1.417539
beta3_yellow 3 1.396072
beta0_pH 4 1.373773
beta1_pelagic 6 1.287940
beta2_yellow 4 1.279573
parameter n badRhat_avg
beta1_yellow 4 1.271463
beta0_pelagic 5 1.255507
beta2_pH 9 1.237475
beta1_pH 14 1.222073
beta0_yellow 5 1.179116
tau_beta0_yellow 3 1.155369
tau_beta0_pH 1 1.148075
mu_beta0_pH 1 1.140191
beta4_yellow 1 1.122017
beta3_pelagic 1 1.112629
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta0_pelagic 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 1
beta0_pH 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0
beta0_yellow 0 0 0 1 0 0 0 0 0 1 1 1 0 0 0 1
beta1_black 1 0 1 1 1 1 1 1 0 1 1 0 1 1 1 0
beta1_pelagic 0 0 1 1 0 0 1 0 0 0 1 0 0 0 1 1
beta1_pH 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0
beta1_yellow 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0
beta2_black 0 0 1 1 0 1 0 0 1 1 0 0 0 1 0 0
beta2_pelagic 1 1 0 1 1 0 0 1 0 0 0 0 1 1 1 1
beta2_pH 1 0 0 0 0 1 0 0 1 1 0 1 0 1 0 0
beta2_yellow 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 0
beta3_black 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
beta3_pH 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0
beta3_yellow 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 0
beta4_yellow 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.130 0.074 -0.268 -0.132 0.027
mu_bc_H[2] -0.092 0.046 -0.169 -0.097 0.011
mu_bc_H[3] -0.437 0.069 -0.566 -0.437 -0.298
mu_bc_H[4] -0.995 0.188 -1.377 -0.989 -0.635
mu_bc_H[5] 0.951 0.952 -0.152 0.752 3.292
mu_bc_H[6] -2.152 0.324 -2.778 -2.150 -1.493
mu_bc_H[7] -0.454 0.112 -0.684 -0.449 -0.247
mu_bc_H[8] 0.240 0.357 -0.337 0.206 1.013
mu_bc_H[9] -0.300 0.138 -0.557 -0.302 -0.021
mu_bc_H[10] -0.111 0.069 -0.236 -0.113 0.036
mu_bc_H[11] -0.124 0.037 -0.195 -0.124 -0.051
mu_bc_H[12] -0.252 0.106 -0.479 -0.250 -0.052
mu_bc_H[13] -0.137 0.080 -0.292 -0.139 0.020
mu_bc_H[14] -0.304 0.098 -0.496 -0.302 -0.116
mu_bc_H[15] -0.344 0.050 -0.440 -0.344 -0.246
mu_bc_H[16] -0.274 0.367 -0.924 -0.302 0.548
mu_bc_R[1] 1.295 0.144 1.019 1.294 1.583
mu_bc_R[2] 1.452 0.094 1.266 1.454 1.640
mu_bc_R[3] 1.382 0.137 1.106 1.386 1.646
mu_bc_R[4] 0.937 0.197 0.522 0.945 1.296
mu_bc_R[5] 1.151 0.472 0.233 1.164 2.053
mu_bc_R[6] -1.598 0.429 -2.449 -1.606 -0.773
mu_bc_R[7] 0.290 0.189 -0.076 0.287 0.664
mu_bc_R[8] 0.552 0.201 0.145 0.553 0.938
mu_bc_R[9] 0.332 0.207 -0.106 0.341 0.698
mu_bc_R[10] 1.327 0.127 1.068 1.331 1.568
mu_bc_R[11] 1.040 0.098 0.839 1.040 1.231
mu_bc_R[12] 0.830 0.207 0.423 0.835 1.225
mu_bc_R[13] 1.028 0.103 0.820 1.030 1.235
mu_bc_R[14] 0.901 0.147 0.600 0.905 1.173
mu_bc_R[15] 0.780 0.109 0.570 0.783 0.987
mu_bc_R[16] 1.089 0.127 0.844 1.089 1.330
tau_pH[1] 5.010 0.768 3.253 5.175 6.201
tau_pH[2] 2.531 0.313 2.004 2.508 3.217
tau_pH[3] 2.177 0.249 1.704 2.176 2.678
beta0_pH[1,1] 0.530 0.182 0.181 0.534 0.884
beta0_pH[2,1] 1.349 0.193 0.954 1.352 1.732
beta0_pH[3,1] 1.417 0.198 0.994 1.428 1.766
beta0_pH[4,1] 1.593 0.209 1.154 1.602 1.971
beta0_pH[5,1] -0.822 0.310 -1.501 -0.818 -0.242
beta0_pH[6,1] -0.643 0.462 -1.817 -0.554 0.024
beta0_pH[7,1] 0.100 0.650 -1.196 0.123 0.925
beta0_pH[8,1] -0.656 0.312 -1.345 -0.618 -0.166
beta0_pH[9,1] -0.601 0.304 -1.305 -0.581 -0.059
beta0_pH[10,1] 0.210 0.195 -0.179 0.210 0.591
beta0_pH[11,1] -0.089 0.181 -0.444 -0.090 0.272
beta0_pH[12,1] 0.511 0.197 0.130 0.513 0.898
beta0_pH[13,1] 0.030 0.157 -0.277 0.026 0.338
beta0_pH[14,1] -0.306 0.169 -0.645 -0.302 0.015
beta0_pH[15,1] 0.217 0.611 -0.369 0.003 1.703
beta0_pH[16,1] -0.467 0.354 -1.260 -0.416 0.085
beta0_pH[1,2] 2.589 0.244 2.066 2.617 2.996
beta0_pH[2,2] 2.690 0.295 1.978 2.769 3.098
beta0_pH[3,2] 2.396 0.283 1.805 2.417 2.910
beta0_pH[4,2] 2.543 0.343 1.839 2.611 3.040
beta0_pH[5,2] 4.477 1.454 2.473 4.202 8.100
beta0_pH[6,2] 2.872 0.281 2.318 2.883 3.376
beta0_pH[7,2] 1.914 0.193 1.525 1.928 2.237
beta0_pH[8,2] 2.803 0.224 2.401 2.826 3.146
beta0_pH[9,2] 3.001 0.576 1.634 3.203 3.740
beta0_pH[10,2] 3.680 0.216 3.210 3.687 4.072
beta0_pH[11,2] -4.884 0.280 -5.443 -4.877 -4.338
beta0_pH[12,2] -4.851 0.417 -5.722 -4.837 -4.076
beta0_pH[13,2] -4.607 0.393 -5.373 -4.613 -3.820
beta0_pH[14,2] -5.702 0.461 -6.665 -5.683 -4.844
beta0_pH[15,2] -4.243 0.323 -4.864 -4.248 -3.594
beta0_pH[16,2] -4.886 0.378 -5.651 -4.885 -4.151
beta0_pH[1,3] 0.467 0.617 -0.913 0.544 1.353
beta0_pH[2,3] 1.860 0.515 0.464 2.022 2.460
beta0_pH[3,3] 2.289 0.351 1.354 2.372 2.736
beta0_pH[4,3] 2.709 0.488 1.263 2.841 3.223
beta0_pH[5,3] 1.013 1.869 -1.998 0.754 5.617
beta0_pH[6,3] -0.741 1.173 -3.081 -0.831 1.500
beta0_pH[7,3] -2.357 0.712 -4.066 -2.257 -1.246
beta0_pH[8,3] 0.237 0.200 -0.161 0.238 0.615
beta0_pH[9,3] -1.095 0.757 -2.866 -0.856 -0.092
beta0_pH[10,3] -0.583 1.019 -2.590 -0.571 0.986
beta0_pH[11,3] -0.162 0.314 -0.739 -0.178 0.478
beta0_pH[12,3] -0.844 0.358 -1.593 -0.828 -0.197
beta0_pH[13,3] -0.105 0.317 -0.705 -0.112 0.549
beta0_pH[14,3] -0.263 0.280 -0.802 -0.258 0.279
beta0_pH[15,3] -0.544 0.418 -1.241 -0.583 0.370
beta0_pH[16,3] -0.369 0.297 -0.957 -0.368 0.227
beta1_pH[1,1] 3.085 0.333 2.465 3.076 3.788
beta1_pH[2,1] 2.191 0.300 1.641 2.178 2.826
beta1_pH[3,1] 2.033 0.327 1.513 2.000 2.780
beta1_pH[4,1] 2.360 0.331 1.798 2.332 3.099
beta1_pH[5,1] 2.281 0.372 1.658 2.247 3.143
beta1_pH[6,1] 3.792 1.148 2.181 3.529 6.532
beta1_pH[7,1] 2.160 1.653 0.308 2.091 5.133
beta1_pH[8,1] 3.992 1.065 2.521 3.771 6.742
beta1_pH[9,1] 2.274 0.382 1.604 2.241 3.154
beta1_pH[10,1] 2.422 0.272 1.892 2.424 2.953
beta1_pH[11,1] 3.265 0.234 2.814 3.262 3.741
beta1_pH[12,1] 2.526 0.233 2.056 2.523 2.956
beta1_pH[13,1] 2.948 0.221 2.510 2.954 3.370
beta1_pH[14,1] 3.409 0.226 2.981 3.407 3.865
beta1_pH[15,1] 2.686 1.397 1.575 2.557 4.337
beta1_pH[16,1] 4.167 0.691 3.185 4.042 5.803
beta1_pH[1,2] 3.331 12.681 0.007 0.978 26.642
beta1_pH[2,2] 2.930 10.368 0.005 0.887 25.055
beta1_pH[3,2] 1.196 0.343 0.572 1.186 1.875
beta1_pH[4,2] 2.356 8.070 0.081 0.988 13.881
beta1_pH[5,2] 2.049 7.166 0.000 0.223 16.092
beta1_pH[6,2] 0.994 1.186 0.000 0.919 2.592
beta1_pH[7,2] 0.768 1.415 0.000 0.178 4.935
beta1_pH[8,2] 1.472 11.805 0.000 0.235 10.112
beta1_pH[9,2] 1.211 5.929 0.000 0.205 2.983
beta1_pH[10,2] 9.881 32.288 0.000 2.146 75.858
beta1_pH[11,2] 6.737 0.308 6.133 6.734 7.368
beta1_pH[12,2] 6.588 0.518 5.688 6.547 7.781
beta1_pH[13,2] 7.038 0.429 6.192 7.038 7.907
beta1_pH[14,2] 7.372 0.482 6.495 7.347 8.369
beta1_pH[15,2] 6.757 0.350 6.080 6.763 7.451
beta1_pH[16,2] 7.523 0.413 6.731 7.524 8.352
beta1_pH[1,3] 3.133 1.230 1.614 2.839 6.450
beta1_pH[2,3] 2.185 5.591 0.001 0.625 19.897
beta1_pH[3,3] 0.790 2.286 0.000 0.290 4.702
beta1_pH[4,3] 1.615 3.829 0.000 0.377 14.231
beta1_pH[5,3] 4.404 6.357 1.597 3.432 11.808
beta1_pH[6,3] 2.901 1.442 1.048 2.734 5.535
beta1_pH[7,3] 3.217 0.729 2.085 3.104 4.923
beta1_pH[8,3] 2.890 0.415 2.170 2.870 3.734
beta1_pH[9,3] 3.200 0.771 2.105 3.021 4.995
beta1_pH[10,3] 4.009 1.088 2.370 3.938 6.253
beta1_pH[11,3] 2.738 0.377 1.964 2.740 3.478
beta1_pH[12,3] 4.091 0.445 3.241 4.082 4.974
beta1_pH[13,3] 1.684 0.340 0.994 1.691 2.334
beta1_pH[14,3] 2.494 0.352 1.791 2.488 3.170
beta1_pH[15,3] 1.797 0.492 0.671 1.869 2.609
beta1_pH[16,3] 1.761 0.331 1.092 1.768 2.402
beta2_pH[1,1] 0.480 0.136 0.289 0.457 0.804
beta2_pH[2,1] 0.564 0.337 0.234 0.497 1.275
beta2_pH[3,1] 0.617 0.435 0.204 0.524 1.747
beta2_pH[4,1] 0.488 0.235 0.220 0.448 0.964
beta2_pH[5,1] 1.260 1.055 0.219 0.958 3.957
beta2_pH[6,1] 0.197 0.088 0.089 0.181 0.397
beta2_pH[7,1] -0.250 1.311 -4.122 0.032 1.538
beta2_pH[8,1] 0.255 0.120 0.120 0.233 0.505
beta2_pH[9,1] 0.446 0.222 0.184 0.400 0.992
beta2_pH[10,1] 0.602 0.271 0.294 0.545 1.247
beta2_pH[11,1] 0.797 0.249 0.473 0.751 1.391
beta2_pH[12,1] 1.492 0.699 0.759 1.308 3.384
beta2_pH[13,1] 0.762 0.296 0.416 0.708 1.428
beta2_pH[14,1] 0.859 0.300 0.523 0.811 1.473
beta2_pH[15,1] 0.351 1.181 -3.842 0.696 1.390
beta2_pH[16,1] 0.365 0.171 0.160 0.320 0.800
beta2_pH[1,2] -0.965 4.094 -9.252 -0.676 6.557
beta2_pH[2,2] -2.175 3.903 -10.422 -2.261 5.896
beta2_pH[3,2] -3.694 2.565 -9.890 -3.073 -0.591
beta2_pH[4,2] -3.326 2.643 -9.908 -2.838 -0.107
beta2_pH[5,2] -2.373 3.824 -9.579 -2.582 5.670
beta2_pH[6,2] -3.223 3.379 -10.085 -3.090 4.335
beta2_pH[7,2] -3.049 3.498 -9.918 -3.044 5.474
beta2_pH[8,2] -2.840 3.745 -10.153 -2.922 5.690
beta2_pH[9,2] -3.050 3.301 -9.367 -3.125 4.139
beta2_pH[10,2] -3.651 3.518 -10.887 -3.565 4.259
beta2_pH[11,2] -7.209 2.628 -13.877 -6.670 -3.746
beta2_pH[12,2] -4.195 2.822 -10.796 -3.758 -0.677
beta2_pH[13,2] -4.353 2.470 -10.384 -3.757 -1.452
beta2_pH[14,2] -5.498 2.516 -11.695 -4.990 -2.114
beta2_pH[15,2] -6.874 2.602 -13.267 -6.346 -3.367
beta2_pH[16,2] -7.226 2.590 -13.802 -6.718 -3.670
beta2_pH[1,3] 1.264 1.922 0.126 0.436 7.036
beta2_pH[2,3] 0.535 3.385 -6.711 0.513 7.921
beta2_pH[3,3] -0.059 3.438 -7.055 -0.096 7.342
beta2_pH[4,3] -0.069 3.102 -5.736 -0.248 7.164
beta2_pH[5,3] 3.082 2.837 -0.357 2.471 10.004
beta2_pH[6,3] 3.005 2.929 -0.534 2.223 10.131
beta2_pH[7,3] 2.900 2.555 0.419 2.005 9.592
beta2_pH[8,3] 4.473 2.941 0.636 3.985 11.443
beta2_pH[9,3] 2.719 2.749 0.289 1.543 9.532
beta2_pH[10,3] 1.700 2.300 0.289 0.628 8.577
beta2_pH[11,3] -2.061 1.523 -6.278 -1.642 -0.594
beta2_pH[12,3] -2.244 1.458 -6.492 -1.839 -0.916
beta2_pH[13,3] -2.792 1.954 -8.214 -2.164 -0.806
beta2_pH[14,3] -2.578 1.821 -8.315 -2.002 -0.841
beta2_pH[15,3] -1.707 2.468 -6.945 -1.862 3.807
beta2_pH[16,3] -2.900 1.968 -8.687 -2.246 -0.858
beta3_pH[1,1] 35.809 0.840 34.222 35.775 37.569
beta3_pH[2,1] 33.618 1.232 31.556 33.490 36.525
beta3_pH[3,1] 33.879 1.302 31.730 33.788 36.624
beta3_pH[4,1] 33.901 1.278 31.665 33.823 36.559
beta3_pH[5,1] 28.067 1.549 26.435 27.617 32.441
beta3_pH[6,1] 38.686 3.071 33.072 38.500 45.043
beta3_pH[7,1] 30.027 9.518 18.411 27.694 45.693
beta3_pH[8,1] 39.952 2.150 36.291 39.708 45.015
beta3_pH[9,1] 30.793 1.529 28.063 30.716 34.049
beta3_pH[10,1] 32.661 0.866 31.028 32.620 34.464
beta3_pH[11,1] 30.347 0.479 29.462 30.347 31.301
beta3_pH[12,1] 30.218 0.414 29.388 30.222 31.051
beta3_pH[13,1] 33.225 0.611 32.073 33.209 34.501
beta3_pH[14,1] 32.034 0.474 31.132 32.028 32.989
beta3_pH[15,1] 29.456 4.327 18.345 31.119 32.497
beta3_pH[16,1] 32.280 1.231 30.538 32.059 35.357
beta3_pH[1,2] 32.636 8.957 18.591 33.226 44.431
beta3_pH[2,2] 25.852 6.822 18.295 23.374 43.725
beta3_pH[3,2] 41.767 1.860 39.722 41.887 44.112
beta3_pH[4,2] 33.535 8.392 19.680 36.790 44.260
beta3_pH[5,2] 30.522 8.072 18.563 29.814 44.947
beta3_pH[6,2] 33.361 5.938 19.099 35.130 44.288
beta3_pH[7,2] 28.657 7.439 18.422 27.520 44.539
beta3_pH[8,2] 28.961 7.455 18.423 27.777 44.596
beta3_pH[9,2] 35.189 9.454 18.681 37.777 45.636
beta3_pH[10,2] 29.413 5.383 19.063 29.490 42.761
beta3_pH[11,2] 43.390 0.149 43.146 43.374 43.716
beta3_pH[12,2] 43.183 0.206 42.717 43.174 43.600
beta3_pH[13,2] 43.829 0.145 43.492 43.855 44.060
beta3_pH[14,2] 43.313 0.161 43.079 43.287 43.693
beta3_pH[15,2] 43.396 0.161 43.131 43.380 43.737
beta3_pH[16,2] 43.501 0.161 43.206 43.501 43.808
beta3_pH[1,3] 38.480 2.332 33.811 38.854 43.154
beta3_pH[2,3] 30.145 7.657 18.543 30.265 44.987
beta3_pH[3,3] 29.718 8.459 18.367 28.431 44.861
beta3_pH[4,3] 27.810 7.727 18.347 25.585 44.676
beta3_pH[5,3] 26.460 6.573 18.312 24.909 42.100
beta3_pH[6,3] 27.383 6.736 18.573 25.709 44.274
beta3_pH[7,3] 26.422 1.001 24.669 26.315 28.685
beta3_pH[8,3] 41.518 0.449 40.717 41.496 42.471
beta3_pH[9,3] 32.288 1.805 27.758 33.088 34.247
beta3_pH[10,3] 34.195 1.590 31.226 34.132 36.645
beta3_pH[11,3] 41.807 0.785 40.245 41.840 43.235
beta3_pH[12,3] 41.722 0.393 40.944 41.734 42.496
beta3_pH[13,3] 42.703 0.876 41.029 42.698 44.577
beta3_pH[14,3] 41.103 0.596 39.867 41.133 42.215
beta3_pH[15,3] 40.134 5.014 29.154 42.415 43.635
beta3_pH[16,3] 42.871 0.752 41.152 42.977 44.085
beta0_pelagic[1] 1.895 0.441 0.721 2.042 2.416
beta0_pelagic[2] 1.203 0.503 -0.372 1.383 1.690
beta0_pelagic[3] 0.152 0.479 -1.124 0.253 0.661
beta0_pelagic[4] 0.327 0.324 -0.454 0.361 0.887
beta0_pelagic[5] 0.527 1.230 -2.822 1.057 1.475
beta0_pelagic[6] 1.271 0.385 0.244 1.381 1.713
beta0_pelagic[7] 1.562 0.202 1.101 1.584 1.849
beta0_pelagic[8] 1.698 0.218 1.217 1.723 1.988
beta0_pelagic[9] 2.357 0.600 0.873 2.592 2.967
beta0_pelagic[10] 2.504 0.250 1.695 2.548 2.789
beta0_pelagic[11] 0.047 0.459 -0.916 0.086 0.685
beta0_pelagic[12] 1.685 0.141 1.403 1.686 1.961
beta0_pelagic[13] 0.323 0.196 -0.097 0.338 0.669
beta0_pelagic[14] -0.158 0.290 -0.785 -0.135 0.336
beta0_pelagic[15] -0.256 0.132 -0.515 -0.257 0.000
beta0_pelagic[16] 0.186 0.313 -0.613 0.270 0.596
beta1_pelagic[1] 0.358 0.445 0.000 0.157 1.563
beta1_pelagic[2] 0.358 0.492 0.000 0.144 1.861
beta1_pelagic[3] 0.956 0.757 0.338 0.776 3.238
beta1_pelagic[4] 0.841 0.337 0.195 0.817 1.604
beta1_pelagic[5] 0.685 1.320 0.000 0.002 4.328
beta1_pelagic[6] 0.283 0.493 0.000 0.003 1.548
beta1_pelagic[7] 0.337 1.388 0.000 0.001 5.072
beta1_pelagic[8] 0.089 0.328 0.000 0.001 0.970
beta1_pelagic[9] 0.465 0.725 0.000 0.006 2.209
beta1_pelagic[10] 0.119 0.505 0.000 0.001 1.129
beta1_pelagic[11] 3.691 1.042 2.200 3.613 5.929
beta1_pelagic[12] 2.803 0.290 2.249 2.798 3.370
beta1_pelagic[13] 2.912 0.751 1.773 2.790 4.674
beta1_pelagic[14] 4.498 1.150 2.829 4.291 7.124
beta1_pelagic[15] 2.911 0.249 2.423 2.917 3.410
beta1_pelagic[16] 3.864 0.995 2.738 3.462 6.359
beta2_pelagic[1] 2.527 2.860 -3.295 2.396 8.574
beta2_pelagic[2] 2.645 2.894 -3.196 2.390 8.895
beta2_pelagic[3] 2.557 2.418 0.063 1.953 8.727
beta2_pelagic[4] 3.073 1.982 0.342 3.172 8.097
beta2_pelagic[5] 0.042 4.660 -8.335 -0.437 9.385
beta2_pelagic[6] 1.199 4.347 -7.779 1.468 9.219
beta2_pelagic[7] 0.348 4.872 -7.472 0.208 8.676
beta2_pelagic[8] 0.491 4.582 -8.149 0.544 9.218
beta2_pelagic[9] 1.135 4.383 -7.951 1.271 9.534
beta2_pelagic[10] 0.759 4.633 -8.281 0.940 9.519
beta2_pelagic[11] 1.202 1.910 0.118 0.269 6.910
beta2_pelagic[12] 4.058 2.170 1.194 3.579 9.325
beta2_pelagic[13] 0.773 1.027 0.194 0.477 3.351
beta2_pelagic[14] 0.300 0.138 0.148 0.271 0.642
beta2_pelagic[15] 3.977 2.080 1.474 3.545 9.288
beta2_pelagic[16] 1.713 2.063 0.175 1.153 7.883
beta3_pelagic[1] 26.378 7.101 18.382 23.593 44.039
beta3_pelagic[2] 27.786 8.256 18.203 24.987 45.049
beta3_pelagic[3] 29.503 3.855 21.839 29.792 38.245
beta3_pelagic[4] 25.802 2.230 21.502 25.909 30.318
beta3_pelagic[5] 33.035 9.626 18.541 32.527 45.985
beta3_pelagic[6] 30.387 7.226 18.670 30.036 44.229
beta3_pelagic[7] 29.344 7.964 18.407 28.296 44.900
beta3_pelagic[8] 29.487 8.079 18.405 28.263 45.051
beta3_pelagic[9] 29.533 7.001 18.638 28.106 44.322
beta3_pelagic[10] 29.219 8.066 18.353 27.999 44.930
beta3_pelagic[11] 42.357 2.007 36.585 42.943 45.098
beta3_pelagic[12] 43.454 0.246 43.004 43.445 43.941
beta3_pelagic[13] 42.783 1.272 40.439 42.703 45.514
beta3_pelagic[14] 42.401 1.693 39.324 42.307 45.754
beta3_pelagic[15] 43.127 0.246 42.518 43.151 43.547
beta3_pelagic[16] 42.944 0.907 40.804 43.051 44.796
mu_beta0_pelagic[1] 0.863 0.831 -0.893 0.873 2.546
mu_beta0_pelagic[2] 1.624 0.610 0.124 1.709 2.634
mu_beta0_pelagic[3] 0.291 0.475 -0.703 0.304 1.233
tau_beta0_pelagic[1] 1.594 4.439 0.063 0.696 7.066
tau_beta0_pelagic[2] 2.019 3.194 0.090 1.372 7.102
tau_beta0_pelagic[3] 1.502 1.164 0.173 1.217 4.577
beta0_yellow[1] -0.543 0.186 -0.967 -0.524 -0.250
beta0_yellow[2] 0.467 0.211 -0.059 0.490 0.780
beta0_yellow[3] -0.350 0.282 -1.009 -0.320 0.033
beta0_yellow[4] 0.655 0.429 -0.526 0.773 1.163
beta0_yellow[5] -1.240 0.410 -2.047 -1.241 -0.433
beta0_yellow[6] 0.267 0.216 -0.163 0.266 0.678
beta0_yellow[7] 0.990 0.345 -0.315 1.040 1.340
beta0_yellow[8] 0.658 0.690 -1.322 0.920 1.270
beta0_yellow[9] -0.107 0.286 -0.636 -0.107 0.405
beta0_yellow[10] 0.232 0.155 -0.073 0.231 0.539
beta0_yellow[11] -1.824 0.560 -2.832 -1.852 -0.305
beta0_yellow[12] -3.649 0.425 -4.541 -3.627 -2.872
beta0_yellow[13] -3.816 0.479 -4.851 -3.780 -3.014
beta0_yellow[14] -2.023 0.722 -3.140 -2.130 -0.074
beta0_yellow[15] -2.893 0.392 -3.721 -2.891 -2.125
beta0_yellow[16] -2.422 0.451 -3.334 -2.426 -1.496
beta1_yellow[1] 0.448 0.561 0.000 0.255 1.868
beta1_yellow[2] 1.190 0.576 0.603 1.076 3.228
beta1_yellow[3] 0.748 0.546 0.043 0.669 2.174
beta1_yellow[4] 1.874 1.139 0.708 1.458 4.923
beta1_yellow[5] 3.851 5.947 1.332 2.941 10.614
beta1_yellow[6] 2.270 0.359 1.546 2.276 2.975
beta1_yellow[7] 8.618 9.303 1.255 5.205 36.118
beta1_yellow[8] 2.522 3.785 0.014 1.721 13.077
beta1_yellow[9] 1.567 0.458 0.827 1.530 2.496
beta1_yellow[10] 2.363 0.507 1.498 2.325 3.396
beta1_yellow[11] 2.023 0.483 1.044 2.017 2.959
beta1_yellow[12] 2.455 0.432 1.653 2.431 3.368
beta1_yellow[13] 2.936 0.485 2.105 2.906 3.997
beta1_yellow[14] 2.202 0.608 0.788 2.207 3.293
beta1_yellow[15] 2.150 0.380 1.390 2.138 2.935
beta1_yellow[16] 2.177 0.447 1.282 2.181 3.091
beta2_yellow[1] -1.615 2.294 -7.312 -1.269 2.735
beta2_yellow[2] -2.174 2.103 -7.685 -1.586 -0.110
beta2_yellow[3] -2.071 2.018 -7.250 -1.699 -0.041
beta2_yellow[4] -1.094 1.376 -4.545 -0.436 -0.062
beta2_yellow[5] -4.128 2.846 -10.836 -3.580 -0.502
beta2_yellow[6] 3.581 2.167 0.970 3.074 9.129
beta2_yellow[7] -4.384 3.144 -11.534 -4.047 1.954
beta2_yellow[8] -1.761 4.099 -10.051 -1.575 6.953
beta2_yellow[9] 3.743 2.400 0.272 3.381 9.445
beta2_yellow[10] -3.639 2.734 -10.609 -2.777 -0.668
beta2_yellow[11] -3.418 2.901 -9.382 -3.339 3.423
beta2_yellow[12] -3.973 1.912 -8.497 -3.606 -1.322
beta2_yellow[13] -4.052 1.946 -9.147 -3.601 -1.470
beta2_yellow[14] -4.351 2.203 -9.188 -3.885 -1.202
beta2_yellow[15] -3.791 2.146 -9.153 -3.307 -1.076
beta2_yellow[16] -4.431 2.234 -10.026 -3.928 -1.424
beta3_yellow[1] 27.650 7.710 18.305 25.352 44.814
beta3_yellow[2] 28.941 2.307 21.902 28.956 33.051
beta3_yellow[3] 32.468 3.841 20.410 32.843 39.103
beta3_yellow[4] 28.764 4.251 19.686 28.235 37.353
beta3_yellow[5] 33.221 1.747 29.031 33.354 35.938
beta3_yellow[6] 39.672 0.533 38.729 39.631 40.877
beta3_yellow[7] 20.272 2.241 18.421 19.974 26.703
beta3_yellow[8] 25.320 5.943 18.190 24.101 42.152
beta3_yellow[9] 37.805 1.555 36.178 37.594 42.704
beta3_yellow[10] 29.223 0.725 27.571 29.348 30.155
beta3_yellow[11] 43.434 5.054 28.341 45.285 45.963
beta3_yellow[12] 43.353 0.420 42.567 43.325 44.209
beta3_yellow[13] 44.861 0.376 44.042 44.920 45.497
beta3_yellow[14] 43.284 3.584 29.697 44.147 45.815
beta3_yellow[15] 45.193 0.515 44.178 45.187 45.971
beta3_yellow[16] 44.580 0.633 43.430 44.557 45.832
mu_beta0_yellow[1] 0.059 0.535 -0.984 0.043 1.178
mu_beta0_yellow[2] 0.125 0.479 -0.896 0.143 1.063
mu_beta0_yellow[3] -2.384 0.694 -3.438 -2.483 -0.611
tau_beta0_yellow[1] 2.258 3.884 0.098 1.285 9.706
tau_beta0_yellow[2] 1.352 1.974 0.151 0.982 4.434
tau_beta0_yellow[3] 1.333 2.612 0.088 0.765 5.708
beta0_black[1] 0.030 0.183 -0.327 0.032 0.379
beta0_black[2] 1.859 0.184 1.462 1.874 2.139
beta0_black[3] 1.273 0.173 0.910 1.289 1.551
beta0_black[4] 1.989 0.343 0.996 2.023 2.512
beta0_black[5] 1.562 1.961 -3.165 1.655 5.455
beta0_black[6] 1.532 2.016 -2.925 1.631 5.472
beta0_black[7] 1.592 1.988 -2.881 1.611 5.450
beta0_black[8] 1.259 0.232 0.785 1.263 1.692
beta0_black[9] 2.405 0.285 1.847 2.421 2.893
beta0_black[10] 1.463 0.129 1.214 1.467 1.718
beta0_black[11] 3.411 0.243 2.972 3.437 3.747
beta0_black[12] 4.493 0.190 4.124 4.490 4.873
beta0_black[13] -0.075 0.219 -0.534 -0.062 0.326
beta0_black[14] 2.218 0.474 0.867 2.323 2.819
beta0_black[15] 1.185 0.274 0.503 1.226 1.566
beta0_black[16] 4.074 0.539 2.296 4.209 4.559
beta2_black[1] 1.914 3.599 -6.446 2.129 8.821
beta2_black[2] -0.441 3.549 -7.386 -0.656 6.678
beta2_black[3] -0.054 3.997 -7.982 0.033 7.904
beta2_black[4] -2.140 2.635 -8.479 -1.660 2.513
beta2_black[5] -0.331 4.328 -8.719 -0.401 8.653
beta2_black[6] -0.359 4.250 -8.798 -0.387 8.302
beta2_black[7] -0.383 4.333 -9.001 -0.521 8.384
beta2_black[8] -0.408 4.315 -8.656 -0.588 8.439
beta2_black[9] -0.464 4.286 -9.183 -0.445 8.004
beta2_black[10] -0.426 4.461 -9.335 -0.469 8.607
beta2_black[11] -4.712 3.410 -10.717 -5.070 1.938
beta2_black[12] -4.737 2.661 -10.168 -4.474 -0.731
beta2_black[13] -3.964 2.879 -10.466 -3.229 -0.543
beta2_black[14] -4.803 3.729 -10.338 -4.588 -0.111
beta2_black[15] -3.988 3.467 -11.364 -3.578 2.036
beta2_black[16] -3.153 3.949 -10.697 -3.089 4.343
beta3_black[1] 38.081 6.851 19.906 41.269 43.591
beta3_black[2] 30.149 8.194 18.392 29.778 45.022
beta3_black[3] 29.642 7.926 18.402 29.153 44.611
beta3_black[4] 32.596 4.338 19.998 32.801 40.646
beta3_black[5] 29.816 7.839 18.532 28.865 44.795
beta3_black[6] 29.904 7.923 18.414 28.907 44.978
beta3_black[7] 30.142 7.973 18.475 29.201 44.918
beta3_black[8] 29.946 7.967 18.484 29.001 44.776
beta3_black[9] 30.174 8.033 18.451 29.431 44.996
beta3_black[10] 29.800 7.908 18.464 28.852 44.973
beta3_black[11] 29.866 6.975 18.600 29.780 43.358
beta3_black[12] 32.937 1.126 30.976 33.072 33.868
beta3_black[13] 39.372 0.614 37.978 39.424 40.412
beta3_black[14] 38.148 4.043 25.717 39.050 45.107
beta3_black[15] 31.394 7.886 18.656 31.159 44.960
beta3_black[16] 28.540 7.413 18.449 27.242 44.357
beta4_black[1] -0.271 0.187 -0.633 -0.268 0.093
beta4_black[2] 0.249 0.178 -0.099 0.250 0.594
beta4_black[3] -0.936 0.188 -1.303 -0.935 -0.564
beta4_black[4] 0.540 0.226 0.113 0.539 0.987
beta4_black[5] 0.233 2.400 -4.296 0.145 5.089
beta4_black[6] 0.211 2.664 -4.448 0.152 4.953
beta4_black[7] 0.234 2.683 -4.480 0.184 4.963
beta4_black[8] -0.686 0.365 -1.411 -0.683 0.010
beta4_black[9] 1.449 1.029 -0.123 1.316 3.783
beta4_black[10] 0.017 0.178 -0.330 0.017 0.369
beta4_black[11] -0.699 0.205 -1.097 -0.700 -0.297
beta4_black[12] 0.302 0.327 -0.298 0.292 0.985
beta4_black[13] -1.196 0.217 -1.625 -1.195 -0.768
beta4_black[14] -0.129 0.231 -0.578 -0.129 0.314
beta4_black[15] -0.895 0.212 -1.306 -0.896 -0.477
beta4_black[16] -0.589 0.224 -1.032 -0.586 -0.143
mu_beta0_black[1] 1.215 0.837 -0.686 1.243 2.892
mu_beta0_black[2] 1.581 0.903 -0.631 1.639 3.295
mu_beta0_black[3] 2.331 0.960 0.322 2.377 4.138
tau_beta0_black[1] 0.879 0.904 0.064 0.603 3.127
tau_beta0_black[2] 2.087 4.525 0.056 0.857 11.327
tau_beta0_black[3] 0.260 0.177 0.052 0.216 0.727
beta0_dsr[11] -2.896 0.280 -3.438 -2.895 -2.341
beta0_dsr[12] 4.519 0.289 3.991 4.508 5.084
beta0_dsr[13] -1.320 0.280 -1.883 -1.311 -0.795
beta0_dsr[14] -3.654 0.534 -4.695 -3.635 -2.642
beta0_dsr[15] -1.926 0.267 -2.474 -1.925 -1.418
beta0_dsr[16] -2.986 0.358 -3.708 -2.982 -2.285
beta1_dsr[11] 4.831 0.294 4.256 4.833 5.408
beta1_dsr[12] 6.449 7.632 2.258 4.976 18.178
beta1_dsr[13] 2.831 0.301 2.271 2.830 3.411
beta1_dsr[14] 6.318 0.564 5.234 6.297 7.418
beta1_dsr[15] 3.309 0.269 2.766 3.310 3.841
beta1_dsr[16] 5.811 0.373 5.064 5.815 6.546
beta2_dsr[11] -8.322 2.422 -14.018 -7.951 -4.615
beta2_dsr[12] -7.070 2.640 -12.977 -6.902 -2.395
beta2_dsr[13] -6.487 2.738 -12.283 -6.340 -1.521
beta2_dsr[14] -6.089 2.681 -12.034 -5.954 -1.746
beta2_dsr[15] -7.763 2.430 -13.539 -7.469 -3.882
beta2_dsr[16] -7.969 2.385 -13.558 -7.615 -4.374
beta3_dsr[11] 43.497 0.150 43.222 43.494 43.774
beta3_dsr[12] 33.972 0.682 32.158 34.105 34.792
beta3_dsr[13] 43.235 0.279 42.810 43.181 43.835
beta3_dsr[14] 43.335 0.227 43.074 43.264 43.914
beta3_dsr[15] 43.505 0.181 43.181 43.506 43.839
beta3_dsr[16] 43.440 0.155 43.178 43.427 43.759
beta4_dsr[11] 0.580 0.214 0.157 0.580 1.000
beta4_dsr[12] 0.249 0.431 -0.565 0.249 1.137
beta4_dsr[13] -0.171 0.208 -0.577 -0.171 0.219
beta4_dsr[14] 0.154 0.244 -0.350 0.158 0.617
beta4_dsr[15] 0.735 0.211 0.334 0.728 1.163
beta4_dsr[16] 0.139 0.221 -0.293 0.135 0.579
beta0_slope[11] -1.944 0.160 -2.255 -1.943 -1.638
beta0_slope[12] -4.657 0.261 -5.147 -4.656 -4.146
beta0_slope[13] -1.353 0.221 -1.849 -1.335 -0.995
beta0_slope[14] -2.645 0.178 -2.996 -2.643 -2.297
beta0_slope[15] -1.386 0.167 -1.716 -1.386 -1.056
beta0_slope[16] -2.726 0.167 -3.056 -2.729 -2.402
beta1_slope[11] 4.588 0.296 3.994 4.592 5.142
beta1_slope[12] 4.987 0.523 3.964 4.987 6.035
beta1_slope[13] 2.952 0.595 2.257 2.851 4.872
beta1_slope[14] 6.516 0.560 5.446 6.508 7.644
beta1_slope[15] 3.059 0.283 2.495 3.061 3.625
beta1_slope[16] 5.368 0.395 4.597 5.372 6.157
beta2_slope[11] 8.056 2.314 4.463 7.723 13.529
beta2_slope[12] 7.177 2.541 2.721 6.973 12.837
beta2_slope[13] 5.635 3.064 0.347 5.640 11.817
beta2_slope[14] 6.540 2.483 2.444 6.337 12.079
beta2_slope[15] 7.580 2.490 3.575 7.222 13.409
beta2_slope[16] 7.719 2.381 4.007 7.446 13.420
beta3_slope[11] 43.476 0.148 43.204 43.470 43.765
beta3_slope[12] 43.411 0.229 43.063 43.384 43.869
beta3_slope[13] 43.658 0.463 42.900 43.729 44.506
beta3_slope[14] 43.317 0.172 43.095 43.276 43.760
beta3_slope[15] 43.511 0.191 43.166 43.510 43.872
beta3_slope[16] 43.462 0.171 43.174 43.452 43.804
beta4_slope[11] -0.568 0.212 -0.993 -0.567 -0.147
beta4_slope[12] -1.401 0.665 -2.932 -1.334 -0.366
beta4_slope[13] 0.058 0.215 -0.355 0.055 0.487
beta4_slope[14] -0.177 0.255 -0.658 -0.178 0.333
beta4_slope[15] -0.709 0.205 -1.113 -0.704 -0.310
beta4_slope[16] -0.185 0.225 -0.608 -0.189 0.270
sigma_H[1] 0.200 0.054 0.103 0.197 0.314
sigma_H[2] 0.170 0.030 0.118 0.168 0.237
sigma_H[3] 0.196 0.043 0.123 0.193 0.287
sigma_H[4] 0.417 0.078 0.289 0.410 0.593
sigma_H[5] 0.995 0.213 0.611 0.980 1.443
sigma_H[6] 0.386 0.199 0.027 0.378 0.794
sigma_H[7] 0.300 0.060 0.208 0.292 0.439
sigma_H[8] 0.418 0.093 0.277 0.410 0.606
sigma_H[9] 0.522 0.127 0.326 0.505 0.811
sigma_H[10] 0.215 0.042 0.144 0.211 0.309
sigma_H[11] 0.278 0.046 0.201 0.274 0.380
sigma_H[12] 0.438 0.168 0.206 0.410 0.793
sigma_H[13] 0.214 0.037 0.149 0.211 0.297
sigma_H[14] 0.508 0.092 0.347 0.502 0.704
sigma_H[15] 0.247 0.041 0.179 0.243 0.337
sigma_H[16] 0.225 0.044 0.150 0.221 0.320
lambda_H[1] 3.141 4.135 0.192 1.774 14.251
lambda_H[2] 8.147 7.247 0.724 6.022 26.355
lambda_H[3] 6.252 9.732 0.235 3.068 36.035
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 4.106 9.386 0.042 1.021 30.498
lambda_H[6] 8.394 16.324 0.007 1.343 54.825
lambda_H[7] 0.013 0.009 0.002 0.011 0.039
lambda_H[8] 8.367 10.449 0.124 4.780 36.084
lambda_H[9] 0.015 0.010 0.003 0.013 0.042
lambda_H[10] 0.337 1.059 0.032 0.205 1.147
lambda_H[11] 0.269 0.410 0.010 0.129 1.321
lambda_H[12] 4.942 6.481 0.203 2.821 21.838
lambda_H[13] 3.467 3.137 0.206 2.585 11.761
lambda_H[14] 3.367 4.173 0.225 2.048 13.997
lambda_H[15] 0.029 0.210 0.004 0.017 0.104
lambda_H[16] 0.892 1.274 0.044 0.467 4.204
mu_lambda_H[1] 4.347 1.888 1.275 4.166 8.626
mu_lambda_H[2] 3.916 1.953 0.712 3.773 8.060
mu_lambda_H[3] 3.498 1.852 0.735 3.244 7.636
sigma_lambda_H[1] 8.632 4.275 2.140 8.044 18.309
sigma_lambda_H[2] 8.575 4.681 1.320 8.002 18.434
sigma_lambda_H[3] 6.233 3.939 1.023 5.372 15.946
beta_H[1,1] 6.940 1.032 4.456 7.098 8.554
beta_H[2,1] 9.867 0.492 8.744 9.901 10.743
beta_H[3,1] 7.983 0.803 5.958 8.095 9.288
beta_H[4,1] 9.335 7.845 -6.380 9.436 24.474
beta_H[5,1] 0.137 2.314 -4.829 0.329 4.193
beta_H[6,1] 3.203 4.058 -7.401 4.630 7.612
beta_H[7,1] 0.515 5.672 -11.729 0.902 10.625
beta_H[8,1] 1.394 4.108 -2.325 1.250 3.597
beta_H[9,1] 13.139 5.509 1.996 13.165 24.361
beta_H[10,1] 7.090 1.667 3.601 7.157 10.336
beta_H[11,1] 5.135 3.505 -2.913 5.906 9.941
beta_H[12,1] 2.614 0.999 0.843 2.545 4.853
beta_H[13,1] 9.042 0.952 6.857 9.122 10.524
beta_H[14,1] 2.197 1.028 0.198 2.193 4.354
beta_H[15,1] -6.045 3.845 -13.005 -6.296 2.067
beta_H[16,1] 3.394 2.560 -0.813 3.072 9.444
beta_H[1,2] 7.911 0.242 7.428 7.923 8.378
beta_H[2,2] 10.021 0.137 9.746 10.020 10.286
beta_H[3,2] 8.957 0.198 8.566 8.957 9.354
beta_H[4,2] 3.533 1.500 0.642 3.479 6.607
beta_H[5,2] 1.942 0.935 0.076 1.939 3.723
beta_H[6,2] 5.768 1.063 3.230 5.954 7.358
beta_H[7,2] 2.634 1.092 0.682 2.572 4.888
beta_H[8,2] 3.007 1.119 1.403 3.149 4.244
beta_H[9,2] 3.483 1.106 1.346 3.456 5.697
beta_H[10,2] 8.197 0.340 7.475 8.201 8.854
beta_H[11,2] 9.757 0.628 8.832 9.642 11.160
beta_H[12,2] 3.947 0.361 3.273 3.929 4.724
beta_H[13,2] 9.126 0.254 8.673 9.111 9.662
beta_H[14,2] 4.018 0.353 3.335 4.021 4.742
beta_H[15,2] 11.346 0.696 9.880 11.370 12.595
beta_H[16,2] 4.532 0.821 2.957 4.525 6.213
beta_H[1,3] 8.464 0.238 8.028 8.451 8.980
beta_H[2,3] 10.068 0.119 9.836 10.067 10.315
beta_H[3,3] 9.621 0.166 9.316 9.615 9.970
beta_H[4,3] -2.475 0.875 -4.241 -2.466 -0.761
beta_H[5,3] 3.802 0.617 2.481 3.808 4.965
beta_H[6,3] 7.956 1.203 6.332 7.587 10.586
beta_H[7,3] -2.731 0.712 -4.080 -2.754 -1.281
beta_H[8,3] 5.255 0.514 4.656 5.188 6.291
beta_H[9,3] -2.849 0.732 -4.335 -2.817 -1.469
beta_H[10,3] 8.703 0.274 8.177 8.697 9.248
beta_H[11,3] 8.548 0.284 7.961 8.564 9.050
beta_H[12,3] 5.253 0.316 4.547 5.285 5.769
beta_H[13,3] 8.843 0.176 8.477 8.847 9.182
beta_H[14,3] 5.724 0.276 5.138 5.740 6.230
beta_H[15,3] 10.381 0.323 9.746 10.379 11.012
beta_H[16,3] 6.277 0.610 4.960 6.335 7.302
beta_H[1,4] 8.266 0.178 7.891 8.275 8.581
beta_H[2,4] 10.125 0.122 9.873 10.132 10.341
beta_H[3,4] 10.122 0.163 9.765 10.135 10.411
beta_H[4,4] 11.807 0.450 10.905 11.824 12.686
beta_H[5,4] 5.465 0.743 4.275 5.374 7.139
beta_H[6,4] 7.062 0.927 4.911 7.339 8.312
beta_H[7,4] 8.218 0.364 7.512 8.217 8.931
beta_H[8,4] 6.706 0.260 6.205 6.718 7.141
beta_H[9,4] 7.204 0.470 6.266 7.207 8.123
beta_H[10,4] 7.762 0.236 7.315 7.752 8.240
beta_H[11,4] 9.384 0.197 8.996 9.386 9.774
beta_H[12,4] 7.144 0.211 6.741 7.143 7.580
beta_H[13,4] 9.051 0.146 8.761 9.052 9.337
beta_H[14,4] 7.734 0.218 7.283 7.736 8.164
beta_H[15,4] 9.464 0.242 8.978 9.468 9.940
beta_H[16,4] 9.350 0.235 8.920 9.340 9.837
beta_H[1,5] 8.981 0.146 8.690 8.986 9.254
beta_H[2,5] 10.779 0.093 10.601 10.776 10.974
beta_H[3,5] 10.931 0.175 10.612 10.924 11.287
beta_H[4,5] 8.390 0.470 7.488 8.375 9.347
beta_H[5,5] 5.393 0.574 4.048 5.439 6.361
beta_H[6,5] 8.787 0.659 7.896 8.600 10.384
beta_H[7,5] 6.793 0.339 6.143 6.792 7.474
beta_H[8,5] 8.216 0.214 7.866 8.200 8.653
beta_H[9,5] 8.211 0.488 7.225 8.211 9.167
beta_H[10,5] 10.082 0.230 9.630 10.087 10.539
beta_H[11,5] 11.513 0.226 11.071 11.511 11.943
beta_H[12,5] 8.489 0.198 8.122 8.484 8.911
beta_H[13,5] 10.008 0.132 9.757 10.009 10.266
beta_H[14,5] 9.203 0.231 8.773 9.193 9.681
beta_H[15,5] 11.165 0.249 10.675 11.164 11.654
beta_H[16,5] 9.920 0.178 9.557 9.925 10.244
beta_H[1,6] 10.177 0.183 9.859 10.163 10.589
beta_H[2,6] 11.515 0.108 11.301 11.514 11.737
beta_H[3,6] 10.807 0.164 10.463 10.815 11.115
beta_H[4,6] 12.881 0.819 11.282 12.884 14.402
beta_H[5,6] 5.895 0.600 4.753 5.877 7.158
beta_H[6,6] 8.748 0.701 6.781 8.881 9.697
beta_H[7,6] 9.822 0.575 8.667 9.824 10.990
beta_H[8,6] 9.510 0.291 8.992 9.532 9.967
beta_H[9,6] 8.483 0.804 6.907 8.461 10.126
beta_H[10,6] 9.513 0.311 8.850 9.538 10.064
beta_H[11,6] 10.817 0.348 10.090 10.842 11.448
beta_H[12,6] 9.362 0.250 8.867 9.354 9.898
beta_H[13,6] 11.053 0.166 10.759 11.044 11.419
beta_H[14,6] 9.828 0.292 9.223 9.834 10.393
beta_H[15,6] 10.846 0.431 9.995 10.854 11.687
beta_H[16,6] 10.553 0.239 10.043 10.562 10.999
beta_H[1,7] 10.894 0.823 8.900 10.982 12.249
beta_H[2,7] 12.198 0.445 11.224 12.219 13.057
beta_H[3,7] 10.514 0.693 8.931 10.581 11.724
beta_H[4,7] 2.505 4.189 -5.412 2.459 10.936
beta_H[5,7] 6.409 1.793 3.023 6.372 10.357
beta_H[6,7] 9.697 2.547 5.027 9.556 17.022
beta_H[7,7] 10.650 2.862 4.844 10.632 16.400
beta_H[8,7] 10.959 1.078 9.413 10.905 12.752
beta_H[9,7] 4.386 4.106 -4.015 4.600 12.350
beta_H[10,7] 9.847 1.453 7.287 9.761 13.077
beta_H[11,7] 10.979 1.715 7.898 10.847 14.790
beta_H[12,7] 10.019 0.899 8.024 10.106 11.546
beta_H[13,7] 11.666 0.769 9.809 11.774 12.840
beta_H[14,7] 10.416 0.956 8.340 10.481 12.074
beta_H[15,7] 11.922 2.241 7.437 11.874 16.366
beta_H[16,7] 12.259 1.260 10.194 12.079 15.079
beta0_H[1] 8.383 12.642 -18.050 8.615 32.999
beta0_H[2] 10.532 6.398 -2.600 10.688 23.861
beta0_H[3] 10.229 9.899 -10.362 10.175 32.374
beta0_H[4] 6.127 186.107 -378.757 4.392 375.215
beta0_H[5] 4.349 23.984 -42.511 4.325 54.207
beta0_H[6] 6.586 50.489 -101.264 7.562 116.213
beta0_H[7] 4.163 132.956 -266.974 1.811 278.889
beta0_H[8] 5.754 28.443 -15.305 6.510 28.608
beta0_H[9] 6.352 120.181 -239.450 6.300 231.111
beta0_H[10] 7.799 31.788 -56.907 7.650 71.971
beta0_H[11] 8.653 51.000 -96.979 9.331 111.352
beta0_H[12] 6.717 10.918 -15.816 6.742 28.694
beta0_H[13] 9.732 10.645 -12.884 9.777 31.088
beta0_H[14] 7.126 10.940 -15.566 7.286 30.412
beta0_H[15] 5.256 106.851 -216.689 6.436 231.319
beta0_H[16] 8.080 24.879 -41.205 7.950 58.629